We report the alignment and shape of dark matter, stellar, and hot gas distributions in the EAGLE (Evolution and Assembly of GaLaxies and their Environments) and cosmo-OWLS (OverWhelmingly Large Simulations) simulations. The combination of these state-of-the-art hydrodynamical cosmological simulations enables us to span four orders of magnitude in halo mass (11 ≤ log10(M200/[ h-1 M⊙]) ≤ 15), a wide radial range (-2.3 ≤ log10(r/[ h-1 Mpc]) ≤ 1.3) and redshifts 0 ≤ z ≤ 1. The shape parameters of the dark matter, stellar and hot gas distributions follow qualitatively similar trends: they become more aspherical (and triaxial) with increasing halo mass, radius, and redshift. We measure the misalignment of the baryonic components (hot gas and stars) of galaxies with their host halo as a function of halo mass, radius, redshift, and galaxy type (centrals versus satellites and early- versus late-type). Overall, galaxies align well with the local distribution of the total (mostly dark) matter. However, the stellar distributions on galactic scales exhibit a median misalignment of about 45-50 deg with respect to their host haloes. This misalignment is reduced to 25-30 deg in the most massive haloes (13 ≤ log10(M200/[ h-1 M⊙]) ≤ 15). Half of the disc galaxies in the EAGLE simulations have a misalignment angle with respect to their host haloes larger than 40 deg. We present fitting functions and tabulated values for the probability distribution of galaxy-halo misalignment to enable a straightforward inclusion of our results into models of galaxy formations based on purely collisionless N-body simulations.